Quantum mechanics and the Planck-spectrum

[The following is a guest post from Bjoern Malte Schaefer. Bjoern is one of the curators of the Cosmology Question of the Week blog, which is worth checking out. This post is a historical look at some of the early parts in the history of quantum mechanics, in particular, the black-body spectrum. Questions are welcome and I'll make sure he sees any of them. Image captions (and hyper-links, in this case) are, as usual, by me, because guest posters don't ever seem to provide their own.]

Two unusual systems

Quantum mechanics surprises with the statement that the microscopic world works very differently from the macroscopic world. Therefore, it took a while until quantum mechanics was formally established as the theory of the microworld. In particular, despite the fact that two of the natural systems on which theories of quantum mechanics could initially be tested were very simple, even from the point of view of the physicists of the time, one needed to introduce a number of novel concepts for their description. These two physical systems were the hydrogen atom and the spectrum of a thermal radiation source. The hydrogen atom was the lightest of all atoms with the most simply structured spectrum. It exhibited many regularities involving rational numbers relating its discrete energy levels. It could only be ionised once implying that it had only a single electron and from these reasons it was the obvious test case for any theory of mechanics in the quantum regime. Werner Heisenberg was the first to be successful in solving this quantum mechanical analogue of the Kepler-problem, i.e. the equation of motion of a charge moving in a Coulomb-potential, paving the way for a systematic understanding of atomic spectra, their fine structure, the theory of chemical bonds, interactions of atoms with fields and ultimately quantum electrodynamics.

The Planck-spectrum was equally puzzling: It is the distribution of photon energies emitted from a body at thermal equilibrium and does not, in particular, require any further specification of the body apart that it should be black, meaning ideally emitting and absorbing radiation irrespective of wave length: From this point of view it is really the simplest macroscopic body one could imagine because its internal structure does not matter. In contrast to the hydrogen atom it is described with a continuous spectrum. In fact, there are at least two beautiful examples of Planck-spectra in Nature: the thermal spectrum of the Sun and the cosmic microwave background. The solution to the Planck-spectrum involves quantum mechanics, quantum statistics and relativity, and unites three of the four the great constants of Nature: the Planck-quantum h, the Boltzmann-constant \(k_B\) and the speed of light c.

The spectrum (basically intensity against wavelength or frequency) of the light from the sun (in yellow) and a blackbody with the same temperature (grey). I'm actually surprised by how similar they are.

Limits of the Planck-spectrum

Although criticised at the time by many physicists as phenomenological, the high energy part of the Planck-spectrum is relatively straightforward to understand, as had been realised by Wilhelm Wien: Starting with the result that photons as relativistic particles carry energies proportional to their frequency as well as momenta inversely proportional to their wave length (the constant of proportionality in both cases being the Planck-constant h), imposing isotropy of the photon momenta and assuming a thermal distribution of energies according to Boltzmann leads directly to Wien's result which is an excellent fit at high photon energies but shows discrepancies at low photon energies, implying that at low temperatures the system exhibits quantum behaviour of some type.

And now, for something completely different...

[The following is a guest post from Jenn Reuer. I'm kind of excited because this is our first genuine, bona fide, guest post about research by a genuine, bona fide, researcher. Jenn and I attended the same college at Oxford. When I arrived there Jenn was finishing her Masters in English literature. Now she is just finishing the doctorate and has taken time away from that awful phase of one's life to tell us a bit about her research. Enjoy...]

Image credit: The Historical Association

I work on 14th – 15th century Middle English and Older Scots romances about King Arthur. Specifically, I look at the influence of medieval law in shaping ideas about kingship and justice in three poems, and how the interface of literature and law is frequently signposted by the phrase, ‘reason and right.’

(For those of you who might be wondering what I’m on about . . . ‘romance’, in this context, refers to: ‘a tale, in prose or verse, that embodies the adventures of some hero of chivalry, belonging both in matter and form to the ages of knighthood.’)

So, what do fantastic tales about knights, magic and adventures have to do with the fairly dry subject of law? As it turns out, quite a lot. An understanding of law helps us understand why some characters behave the way they do, say what they say, and occasionally, it even make us question the efficacy (and justice) of the norm. Here’s an example of how the use of legal language and procedure can help us approach romance in a new light.

Talking Ghosts and a Question of Ethics

Here commes an errant knight

Do him reson and right

Reminders of the transience of life and earthly

glory is a prevalent motif  in medieval art, 

and is frequently found on tombs. 

Image credit: Morbid Anatomy

The above is a quote from one of the texts that I cover in my thesis, called The Awntyrs off Arthur or, The Adventures of Arthur. (An online version of the poem, complete with a glossary, can be found here.) Remember the phrase, ‘reason and right.’ We’ll be coming back to it later.

In the first half of the poem, Arthur is off on a hunt while Gawain and Queen Guinevere take rest by the Tarn Walding. Here, they end up receiving a few key life lessons from the ghost of Guinevere’s mother.

Its skeletal body caked in mud, sunken eyes glowing like coals and a toad biting into the skull, the ghost preaches (with words and by its very presence) private as well as social responsibility: So as I am, you shall also be. All earthly things are but temporary. Remember the poor while you are still alive, and stay away from sin.

While the message seems somewhat lost on Guinevere, Gawain is led to question the lifestyle of his king and fellow knights:

“How shal we fare," quod the freke, "that fonden to fight,
And thus defoulen the folke on fele kinges londes,
And riches over reymes withouten eny right,
Wynnen worshipp in werre thorgh wightnesse of hondes?"

‘How shall we fare,’ said the warrior, ‘that undertake to fight,
And thus trample over the folk on various kings’ lands
And enter realms without any right
Winning worship in war through prowess of arms?’

Our hero has come to realise that his livelihood and reputation are built on depriving others of their rights. (An important concept, as much of English common law was concerned with the question of who was entitled to what.) How does he reconcile this with the knightly ideal of achieving renown through warfare and acts of violence? The Ghost concludes that Arthur is ‘too covetous,’ and prophesies that once his time atop Fortune’s Wheel is past, he (and Gawain) will meet a tragic end.

Senses of Science

Four months ago I wrote a post about wonder in an attempt to sketch out the aspirational mood of this blog (or at least my sense of it). In six week increments since I’ve metaphorically returned to that mood and tried to make its implications more concrete by mapping out the actual directions that thinking about wonder and new lines of disciplinary mingling have led my own research: first, into the domain of science film, and second, into postulations about this genre within a critical category I called ‘the impossible image.’

So come December, I’ve decided to take the opportunity for reflection provided by the end of a calendar year and circle back to wonder, backlit by a sense of some things I’ve learned from this multi-directional conversation thus far. The hero of this post is an out-and-out iconoclast: the scientist and Surrealist filmmaker Jean Painlevé, whose six-decade career was devoted to the intertwining of science and art on every level. A biologist trained in the Laboratoire d’Anatomie et d’Histologie Comparée at the Sorbonne, Painlevé was an avant-garde photographer and filmmaker who penned countless texts, reviews, polemics, and manifestos; was politically active during and beyond the Second World War; and initiated a scientific film institute dedicated to supporting and disseminating science film well before the nexus of art and science was comprehended as a serious topic.

underwater bricolage: Jean Painlevé with his diving gear
"Everything is the center of the world. I'm forced to be multicentric."

Best of all, Painlevé is a humorist. His mesmerizing films and delicate photographs, chatty texts and sparking interviews give us a way to concretize a subtle quality of the aesthetics of wonder—the significance of pleasure in the strangeness and surprising beauty of the natural world. The mood of his contribution to the history of our topic seems to me perfectly encapsulated in Foucault's riff on discovery and the affects of wonder:

Curiosity is a vice that has been stigmatized in turn by Christianity, by philosophy, and even by a certain conception of science. Curiosity is seen as futility. However, I like the word; it suggests something quite different to me. It evokes "care"; it evokes the care one takes of what exists and what might exist; a sharpened sense of reality, but one that is never immobilized before it; a readiness to find what surrounds us strange and odd; a certain determination to throw off familiar ways of thought and to look at the same things in a different way; a passion for seizing what is happening now and what is disappearing; a lack of respect for the traditional hierarchies of what is important and fundamental.

 

Leonardo: A Painter at the Court of Milan, for the Twenty-First Century

Study of Arms and Hands, c. 1474

Study of a Woman, c. 1490

Earlier this month, one of those once-in-a-lifetime exhibitions opened in London: Leonardo da Vinci: Painter at the Court of Milan. It runs at the National Gallery until early February.

This isn't a review, since I haven't seen the show. But it amazes me that an exhibition like this exists, so consider this another 'live stream' post—a placeholder for reflections and mullings on and around Leonardo's unbelievable images, with some suggestions about why we are seeing more of this work; and subject to being updated with new links, reviews and so on.

To state the obvious, it isn't easy to put together an exhibition like this. In fact there has never been, and will never be, a 'complete' Leonardo retrospective in the manner of a Picasso, a Judd, or a Richter survey—those big, bulky exhibitions that cover the full range of a capacious individual's oeuvre, and of which one can say, with a certain admiration, "I am large, I contain multitudes." These kinds of shows are necessarily overwhelming because they cover a multifaceted life. But in this case the reasons are practical: some of these fifteenth- and sixteenth-century frescoes are site-specific (painted directly on a wall), and they are universally under bureaucratic lock and key: all Leonardo's work, from the most magnificent painting to the quickest, most fleeting of drawings are owed by institutions and individuals (and the Royal Family). So the problems of red tape for any curator contemplating this kind of mountainous show is unimaginable.

Studies of Water passing Obstacles and falling, c. 1508-9

Real time World War II

[Edit: the url to follow this twitter account is this one, https://twitter.com/#!/RealTimeWWII. You don't need your own twitter account to read the page. Also, I somehow convinced myself that yesterday (when I wrote this post) was the 29th, when it was actually the 28th. The Winter War starts on the 30th.]

There is a twitter account that tweets as if it is a news agency reporting World War II live (@RealTimeWW2). I find this account fascinating and have been following it now for more than a month.

The depth and the breadth of what this account adds to one's understanding of the war is actually quite large, so I can only touch the surface in this post. The first thing I noticed was how this method of telling the story of WWII really gives you a much more accurate sense of the timescales involved than you get from reading a history book. Six years is a long time. I discovered the account a few days into the initial German invasion of Poland; Britain and France soon declared war and yet no military action has taken place between any of these nations, apart from a few skirmishes at sea.

It would be foolish to interpret this as somehow making the war boring. Though, in fact, contemporary Britain did make this mistake. There are regular tweets describing British behaviour that makes it obvious why the name they gave this part of the war was the “Phoney War”.

“German pilot who fought off 3 planes to let his crew escape is guest of honour tonight at an RAF dinner in France. Off to POW camp tomorrow”

However, it can be assured that from the perspective of the Poles, the Czechs and the Jews in occupied Germany, this war has been far from phoney so far.

“New German decree: 'Aryans' married to Jews have been given 1 year to divorce their Jewish husband/wife or 'face the consequences'.”

"Occupied Poland: New decree orders all Jews in Krakow to wear an armband with a blue Star of David, as seen being sold: http://pic.twitter.com/GUOdpg8o"

I have toyed with writing a post about this account for a while and decided sometime ago that today would be the day I write the post. Today is the eve of the second major event of The War. That is, the Winter War between Finland and The Soviet Union. Tweets that have gone out in the last 48 hours are ominous and frightening:

“The USSR has renounced its non-aggression treaty with Finland due to "hostile actions"; Moscow radio reports 3 more incidents on border”

The “incidents” were of course incidents that were faked by Soviets on their own outposts to justify military action. By doing such acts their aggression is made more morally ambiguous and their own populace can be made much more supportive of any action.

Three Impossible Images

1.

Marianne Moore, A Jellyfish (1959)

Of course this first one isn’t even an image, but a poem—a lyric. In this digital audio file at the SFMA Poetry Center you can hear Marianne Moore reading it. Listening to this clip is lovely, because it gives you a sense of the witty, self-depreciating charm of the personality behind the language.

If this poem is an ‘image,’ it is a drama of the almost-visible, starring a jellyfish. Quite a specific, individual jellyfish, swimming around as they do, and momentarily caught in a small poetic narrative. It is the jellyfish that is both visible and invisible: fluctuating, transparent, ethereal, sometimes translucent and sometimes highly colored, jewel-toned, gem-like, strangely compelling, very beautiful, intensely desirable, and alive.

The first lines of the poem contain so much all-over movement that you sense the liquidity before articulating it. Yet when the “arm/ approaches” everything changes. Suddenly it hits you that there’s no glass barrier, an aquarium or a zoo, to separate the person from the jellyfish, so that that this might actually be an eco-drama: a story of ecological ethics in which the arm is in the ocean with the jellyfish.

And this realization introduces two important other movements. When the arm drops back it registers fear, but also something else. “Abandon[ing] your intent” isn't exactly giving up. There’s a hint of purposeful letting go: a deliberate act of relinquishment, or an instinctive reaction to the liveness of the jellyfish’s quiver.

This poem is a kind of motionless animation. It is a drama in which what is not visible becomes more practically significant than we can see, so that a very attractive ‘thing’ is not removed from its environment.

Historical Transparency-washing?

[Note from Shaun: the following is a guest post from Matthew Metcalfe. Just like our previous guest poster, Matt and I went to school together. While, at heart, Matt is as kiwi as a 50 cent lolly mixture, he currently lives in Munich. He is also a trained historian. The following is Matt's searching account of an attempt by one of the richest families in Germany, the Quandt dynasty, to transparently(?) reveal their family history.]

"The Rise of the Quandts"

Since I agree with the premise of this blog – the desire to combine the arts and science – I wanted to open up a short chapter on a development out of the circles of German historiography (in German such courses of study belong to the “breadless arts”).

Where most people see politics as current affairs, when you are an historian, you tend to see history everywhere; behind trade deals, bilateral agreements, political and religious conflicts in northern Africa or the Middle East.

If I had to explain how I see the world, for me the world events seem to happen like untidy piles of photos. At any one point you can see the top photos, showing a snapshot of history. But they always overlap, are different sizes and of varying quality and sharpness.

As you pick off the top photos (for most people the current affairs on the news) you see that the motifs are similar but the faces are different. The overlaps and the connections move back and forth as you go through layer on layer.

Three-and-a-half years ago there was an industrial family dynasty where the stack of photos seemed rather short and orderly. The Quandts were a quiet bunch, not talking about their family in detail, typical for tight-knit powerful families. This was all the more interesting because of the sharpness of some of the photos (both real and metaphorical).

For those unfamiliar with the name, the Quandt family, among the richest in Germany, has been the controlling shareholder of BMW since the 1950s. Even though the shareprice is down and analysts are currently saying to buy while it is underpriced, the total fortune of the various family members is estimated at a total of upwards of US30bn, thanks to the wealth of companies they control.

As is the case with many industrial dynasties in Germany, it was safely assumed that the Quandts had profited disproportionately from the policies and crimes perpetrated during the period of National Socialism.

In spite of this, due to the facts that

1. the members of the family directly involved had died before the major wave of investigations into companies were initiated after intense pressure by victim organisations (e.g. companies like Allianz, Deutsche Bank) 
2. the successors to the family fortune had never really wanted to delve into the darker corners of their father’s closet and jealously guarded the archival material,

the exact details of the involvement had never surfaced.

Until, however, a documentary called “The Silence of the Quandts” in 2007, produced and broadcasted by the German broadcaster ARD let off a bombshell and accused the family of intentionally silencing their history and the growth of their fortune, social and political influence on the backs of concentration camp slave labour during WWII.