Spectrum makes beautiful music

Spectrum makes beautiful music

Photo by Sarah Dao on Unsplash

Originally published 18 June 2002

If you’ve seen a rain­bow, you have seen the col­ors of starlight.

The sun is a typ­i­cal star, and the light of oth­er stars also would make earth­ly rain­bows if they weren’t so far away and faint. Astronomers use instru­ments called spec­tro­scopes to make rain­bows of starlight. To the eye, some stars are yel­low like the sun, some red­der, some bluer, but, through a spec­tro­scope, they all reveal a spec­trum of col­ors, of vary­ing intensities.

Now bear with me through some tech­ni­cal stuff and we’ll get to one of the great­est mys­ter­ies of the uni­verse, some­thing so won­der­ful, so unex­pect­ed, we can only shake our heads with awe.

Put sun­light or starlight through a spec­tro­scope and you see some­thing the eye can’t see: The rain­bow has nar­row gaps, miss­ing col­ors of light. The miss­ing col­ors tell us much about stars, includ­ing what stars are made of.

Light is emit­ted and absorbed by atoms. When an atom emits light, atom­ic elec­trons drop down in ener­gy. When an atom absorbs light, elec­trons are boost­ed in energy.

The cru­cial thing about atom­ic elec­trons is this: They can’t have just any old ener­gies. They can only have cer­tain ener­gies — “quan­tized” energies.

Each kind of atom has dif­fer­ent allowed ener­gy lev­els, and these deter­mine the col­ors of light an atom emits or absorbs. Every ele­ment has its own spec­tral “fin­ger­print” of emit­ted or absorbed colors.

These are the “miss­ing col­ors” we see in a solar or stel­lar spec­trum — col­ors absorbed by atoms in the gassy atmos­phere of the star. In the light of stars, we see the same “fin­ger­prints” of absorbed col­ors we see on Earth. And so we know that the entire uni­verse is made of the same ele­ments as Earth.

But why do atom­ic elec­trons have quan­tized ener­gies? Ah, now we approach the mag­i­cal heart of my story.

The first per­son to have a go at find­ing a rule behind the col­or­ful fin­ger­prints of atoms was the great Dan­ish physi­cist Niels Bohr in 1913.

Bohr’s rule worked per­fect­ly for hydro­gen, the sim­plest of the elements.

But his rule was­n’t as pret­ty as physi­cists would like; it seemed too arbi­trary, too uncon­nect­ed to any­thing else.

The less arbi­trary a the­o­ry seems, the hap­pi­er physi­cists are.

Ten years after Bohr, the French physi­cist Louis de Broglie (who was also a musi­cian) showed that Bohr’s rule could be made to seem less arbi­trary if atoms were thought of as lit­tle vibrat­ing musi­cal instru­ments rather than, say, tiny bil­liard balls. The col­ors that an ele­ment emits or absorbs emerge in de Broglie’s the­o­ry in much the same way that a vio­lin string of a cer­tain length, den­si­ty and ten­sion plays only a cer­tain note.

Sud­den­ly, with de Broglie, the lump­ish atoms of the ancients began to sing like a Stradivarius.

Final­ly, in the 1920s, Erwin Schrödinger pro­posed a sin­gle ele­gant equa­tion, a musi­cal sort of equa­tion, that he said would describe the allow­able ener­gy lev­els of every ele­ment — a sin­gle equa­tion in which the entire uni­verse becomes a sort of sym­pho­ny orches­tra, with the ele­ments as the var­i­ous instruments.

Schrödinger’s beau­ti­ful equa­tion can be writ­ten down in half a line, and just look­ing at it you would nev­er guess (if you weren’t a math­e­mati­cian) that it might tell you the miss­ing col­ors in starlight.

But it does. Unfor­tu­nate­ly, the equa­tion is very dif­fi­cult to solve except for the sim­plest atoms, such as hydrogen.

When I used to teach these things, there was noth­ing I liked doing bet­ter with stu­dents than solv­ing Schrödinger’s equa­tion for the hydro­gen atom. It took us sev­er­al class peri­ods. And, lo and behold, when we got to the end, there before us on the black­board were pre­cise­ly, numer­i­cal­ly, the miss­ing col­ors that astronomers see in the light of dis­tant stars.

And here’s the won­der­ful thing, the moral of my sto­ry: That Schrödinger, a mem­ber of the human species on plan­et Earth, in the neigh­bor­hood of a yel­low star, one star of hun­dreds of bil­lions in the Milky Way Galaxy, which is just one of tens of bil­lions of vis­i­ble galax­ies in the uni­verse, can invent a musi­cal sort of equa­tion that in prin­ci­ple — and, to a large extent, in prac­tice — yields upon solu­tion all of the notes of the sym­pho­ny of creation.

Schrödinger, who before his pass­ing, got out of bed, brushed his teeth, and ate break­fast just like you and me. Now if that does­n’t send shiv­ers up your spine, you should go back to bed and for­get that there’s a uni­verse at all.

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