Sunday, December 13, 2015

Von Waldteuffel’s Waffle: A Tale of Gravity & Levity

Mathematics can be tricky. Not only does it describe conditions that are well known and familiar to us – unless you’re careful it may upend convention and restructure matters entirely.

Thus did Professor Klaus von Waldteuffel, Max-Planck-Institut für Gravitationsphysik (Gravitational Physics), discover all on his own and rather by accident.

Von Waldteuffel, a theoretical physicist, spent most of his time pursuing exotic ideas of quantum gravity, fresh concepts that might advance the boundaries of cosmology along with his flagging career.  Among his favorite fancies was “Waldteuffel’s waffle,” the notion that space-time is corrugated, crenellated, creased, and indented with plenty of room for extra dimensions, spare galaxies, and at least ten theoretical descriptive approaches.

Yet deciding which of these ten held the most promise proved daunting, and the project languished. Alone in his small oak-paneled office with paper, pencil, a Nestler model 23 (Mannheim style) slide rule, and quarts of black coffee, von Waldteuffel toiled long hours mulling over the options, each in its turn, again and again, waiting for inspiration and insight.

Then one afternoon, tinkering for the umpteenth time with Einstein’s famous mathematical expressions for general relatively, trying to force symmetry in the case of waffle approach number six, he stumbled upon a stunning and transformative find (or more properly, perhaps, the finding stumbled upon him): an outlandish assortment of geodesics for space-time that, with a prodigious zzZZOT!  and flicker of radiolucency, converted the hapless physicist’s body mass from positive(+) to negative(–).

Plate 1. Illustration of transition from a  
state of positive (+) mass to negative (-)
using the Klein-Möbius manifold model.
Now Einstein’s field equations wouldn’t ordinarily yield negative space-time dimensions this way, i.e., produce gravity in reverse or anti-gravity. Not unless you plugged in negative(–) values for mass which is just what poor Waldteuffel unwittingly did – and imaginary(?) negative values at that! The effect of this action was so singular, so startlingly unaccountable that as if by some quantum legerdemain, the professor was pitched headlong (Plate 1) outside of space-time as we know it (Plate 2) into the strange and hithertofore notional counter-state of negative gravitation (the latter, the consequence of his negative(–) mass) (Plate 3).

And what a peculiar state it was. Instead of the traditional “pull” of gravity, Waldteuffel now experienced a “push,” boosting him aloft with such enthusiasm it might have appeared Nature herself were intent on ejecting him.

“Fräulein Watson, come here. I want you to see this!” he called out excitedly to his office assistant, Ms. Helge Watson of Potsdam.

Yet even with his nose pressed against ceiling plaster, von Waldteuffel wasn’t one to overlook the main opportunity.

Plate 2. Two-dimensional analogy of spacetime distortion 
generated by positive (+) mass.  White lines  represent the 
coordinate system imposed on curved spacetime, which 
would be rectilinear in a flat spacetime. In Newtonian terms, 
this corresponds to gravity.
“I’ll call it levity,” he concluded jubilantly, “the opposite of gravity. Wait’ll they see this at the Astronomische Gesellschaft! No more ‘dreamer with his head in the clouds’ stuff. Now, scientifically speaking at least,  I’ll always have a warm roof and a bed over my head!”

The thought of it got him to laughing out loud.

“Wha….?” exclaimed Ms. Watson, coming up short just then in the office doorway. “Have you…have you been sniffing helium again?”

“Not funny. Find me a rope. I need to get back down there and complete my calculations.”

Ms. Watson quickly composed herself. She was so accustomed to Waldteuffel’s eccentricity that his present predicament hardly surprised her. Now she began to look annoyed.

Plate 3. Two-dimensional analogy of spacetime distortion 
generated by negative (-) mass. White lines  represent the 
coordinate system imposed on curved spacetime, which would
be “negalinear” in a flat spacetime. In science fiction terms, 
this corresponds to levity.
“Even if you’re still, well, up in the air with your theories of space-time, how much more complete could your calculations possibly get?” she queried. “Do you want the rest of creation up there, too?”

“Uh…no, of course not,” replied her boss. “I just have to make sure this is all written down before I forget how I discovered it in the first place. The shift to negative gravity – to levity! [he savored the word] – occurred, you see, even before I'd integrated all the equations.”

Looking skeptical and shaking her head, Ms. Watson backed out hesitantly the way she’d come.

“Whatever you say, sir,” she muttered.

“And it’s nitrous oxide I sniff, not helium,” he called after her from the ceiling. “Please keep that under your hat – and your nose out of it.”

Procuring a length of rope from university building maintenance took Ms. Watson some little time. Not wishing to be thought a lunatic, she purported that the rope was for tying up shipping crates. When a friendly custodian ingenuously offered to help, she momentarily verged on panic, then tactfully but hurriedly demurred.

Arriving back at the office she was in for another surprise. The professor, no longer stuck to the ceiling, lay sprawled across the office carpet, groaning in pain.

“What happened?” she asked as though there were something unusual about gravity.

The office ceiling being rather low, the professor’s ignominious descent resulted in only minor injuries, and he was quickly back on his feet.

“I’m going out for a walk to clear my head,” he announced. “Got to remember just how I arrived at all this and try to make it more stable.”

“Is that really a good idea?” cautioned Ms. Watson anxiously.

But von Waldteuffel was already out the door with his slide rule, notes, pencils and a threadbare Harris tweed. He made it as far as a park bench on the lawn beside Heisenberg Hall, the astrophysics building. Here he sat down and began pumping his slide rule like a jazz trombone, penciling voluminous notations.

By now the sun sagged low on the horizon. From a nearby soccer field came the pulsating beat of a fußball cheerlieder (football cheer songs) rehearsal. 

"Give 'em hell, Tachyons, cis, boom, bah. Goin' past the top tonight, rah, rah, rah."

The professor took no notice but worked ever more feverishly, large drops of sweat standing out on his forehead. Gradually, a delirious, enigmatic grin crept over his face, and his hands began to shake.

Then… zzZZOT!

Twelve thousand feet overhead, a Fairchild-Dornier 328JET on vectored approach to Berlin-Tegel International was suddenly forced into a steep emergency left bank to avoid a midair collision. The pilot’s incident report, citing an “unidentified oddity in rapid ascent” was dismissed as a hoax by civil aviation authorities and prompted a reprimand.

Professor von Waldteuffel, alas, was never seen again.  An expert review of his calculations and notes turned up only gibberish.

Yet for months after his disappearance, the story remained a media sensation. “Waldteuffel zuickerwaffeln” (sugar waffles) were a featured favorite at frühstück (breakfast) restaurants all over Germany until finally displaced by the “Kilometer-hohen stapel von pfannkuchen” (Kilometer-high stack of pancakes). After that, the whole affair was forgotten.

Ms. Watson, having salvaged Professor Waldteuffel's slide rule as a keepsake, took up sniffing nitrous.

"There are many cool things in the universe" -- Swami Deepsheesh Rajathustra